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Proof step 1 from proof del (conclusion)

⊦ mk(rs -- r, f) = mk(rs, f) -- r

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ H0 = H1 ↔ (∀ r. (r ∈ H0 ↔ r ∈ H1) ∧ (r ∈ H0 → H0[r] = H1[r]))
Proof step 3:
⊦ ∀ r0. (r0 ∈ mk(rs -- r, f) ↔ r0 ∈ mk(rs, f) -- r) ∧ (r0 ∈ mk(rs -- r, f) → mk(rs -- r, f)[r0] = (mk(rs, f) -- r)[r0])

Rule argument

spec: heap name: ext seq: ⊦ H0 = H1 ↔ (∀ r. (r ∈ H0 ↔ r ∈ H1) ∧ (r ∈ H0 → H0[r] = H1[r])) subst: [H1, H0] → [mk(rs, f) -- r, mk(rs -- r, f)] flags: <all paths>

Additional information

Used terms: mk(rs, f) -- r, mk(rs -- r, f)